A Satellite Positioning System (SPS), such as the Global Positioning System (GPS) or the Global Orbiting Navigation Satellite System (GLONASS), uses transmission of coded radio signals from a plurality of Earth-orbiting satellites. A single passive receiver of such signals is capable of determining receiver absolute position in an Earth-centered, Earth-fixed coordinate reference system utilized by the SPS. A configuration of two or more receivers can be used to accurately determine the relative positions between the receivers or stations. This method, known as differential positioning, is far more accurate than absolute positioning, provided that the distances between these stations are substantially less than the distances from these stations to the satellites, which is the usual situation.
In differential positioning, many of the errors in the SPS that compromise the accuracy of absolute position determination are similar in magnitude at stations that are physically close. The effect of these errors on the accuracy of differential position determination is therefore substantially reduced by a process of partial error cancellation.
The Global Positioning System (GPS) satellites transmit spread-spectrum signals on the L1 frequency (f.sub.L1 =1575.42 MHz) and on the L2 frequency (f.sub.L2 =1227.6 MHz). The L1 signal is modulated by two pseudo-random noise (PRN) codes, known as the C/A-code (chip rate of 1.023 MHz) and the P-code (chip rate of 10.23 MHz). The L2 signal is modulated only by the P-code. Most GPS receivers generate replica PRN codes to facilitate coherent demodulation of the received GPS signals. Accepted methods for generating the C/A-code and P-code for designers of GPS receivers are discussed in "GPS Interface Control Document ICD-GPS-200", Rockwell International Corporation, Satellite Systems Division, Revision A, Sep. 26, 1984, which is incorporated by reference herein. The operators of the GPS satellites can substitute for the P-code an encrypted version of the P-code, called the Y-code. The Y-code would be transmitted on both the L1 and L2 frequencies.
In addition to transmitting the PRN codes, the GPS satellites also transmit navigation data at 50 baud. These data are ephemerides and almanac of the satellites and are used to calculate accurate satellites positions in an Earth-centered, Earth-fixed coordinate system. These positions are utilized by absolute and differential positioning methods.
The Global Orbiting Navigation Satellite System (GLONASS) satellites transmit spread spectrum signals on channelized L1 frequencies in the band 1597-1617 MHz, and on channelized L2 frequencies in the band 1240-1260 MHz. The choice of L1 and L2 signal frequency is satellite-dependent. The L1 signal is modulated by a C/A-code (chip rate of 511 kHz), and a P-code (chip rate of 5.11 MHz). The L2 signal is currently modulated only by the P-code The GLONASS satellites also transmit navigational data at 50 baud. The methods for receiving the GLONASS signals, and decoding data, are in general similar to those accepted methods for GPS signals.
Numerous applications require the determination of the relative position between stations. Geodetic survey applications can be subdivided into: (1) applications in which all of the stations receiving the satellite signals are stationary, referred to as static surveying; and (2) applications in which one or more of the stations is moving relative to other stations, referred to as kinematic surveying. The latter class of applications is increasingly popular, because many more relative station positions can be determined in a fixed time of observation of the satellites.
If the stations have a method of inter-station communication, the relative positions between stations can be computed in real-time. Satellite data need not be stored and post-processed after a survey mission in applications that require real-time relative position; only the final computed relative positions need to be stored. Techniques which compute relative positions in real-time have the advantage of being able to determine whether any station is experiencing difficulty in receiving the satellite signals--for example, due to equipment failure.
One or more stations is designated as a reference station, and can be fixed at a known position (or can be moving, which is less likely). The positions of the other stations, known as the roving stations, which also may be stationary or moving, are calculated relative to the reference station(s). The approximate absolute position of the reference stations are required. These positions, if not previously determined, can be computed using established absolute position determination methods that utilize measurement of PRN code phases.
The highest accuracy obtainable in differential positioning requires measurement and utilization of the received carrier phase of the L1 and/or L2 signals at precisely known times, derived from clocks within the GPS receivers. Some techniques for processing GPS data for kinematic surveying applications use only these carrier phase measurements in the calculation of differential positions, with measurement of PRN code phases only used to calculate accurate time-marks for the carrier phase measurements. However, other methods also use PRN code phase measurements together with carrier phase measurements in the calculation of differential positions. Such a method is described by Allison in U.S. Pat. No. 5,148,179. A major difficulty occurs if only the carrier phase measurements are utilized in the calculation of differential positions. These measurements are ambiguous. The measurement from each satellite includes the measurement of a fractional phase .PHI.(0.degree..ltoreq..PHI.&lt;360.degree.) plus an additional integer number N of whole cycles of phase. This integer number or integer ambiguity, hereafter referred to as a phase integer, cannot be directly measured by a receiver.
For kinematic surveying, a process known as integer initialization can be used to establish the initially unknown phase integers. One approach is to set the receivers at marks whose relative positions are already known with sufficient accuracy. These relative positions are also known as baselines, and are defined by (x,y,z) vector components. Another approach is to allow the receivers to remain static at arbitrary marks for a selected period of time, to allow static surveying techniques to be used to resolve the phase integers. This method is time consuming. Another approach is to exchange the antennas between receivers set at arbitrary marks which are close together, without disturbing the signal reception during the exchange of the antennas. In this approach, both antennas must be physically moved to different sites, which is a process requiring much care to prevent loss of signal reception.
The methods discussed thus far rely principally on carrier phase measurements to resolve the phase integers. Other methods use a combination of carder phase measurements and PRN code phase measurements to resolve the integers. Such a method is described by Allison in U.S. Pat. No. 5,148,179. Methods which use PRN code phase measurements suffer from problems caused by multi-path errors on the PRN code phase measurements. These problems are worse for techniques which employ only measurements from the L1 signal or the L2 signal and do not combine the L1 and L2 measurements to form useful linear combinations with modified effective signal wavelengths. To enable these methods which use PRN code phase to be used reliably in the presence of multi-path reflections, measurement averaging or filtering is necessary. The necessity for measurement averaging increases the time required to correctly resolve the phase integers.
Once the phase integers are resolved, differential positioning is possible with the full accuracy obtained by the carder phase measurements. However, if signal lock cannot be maintained on at least four satellites, the initialization procedure may need to be repeated.
Several workers have applied two spaced apart antennas for various purposes. U.S. Pat. No. 3,886,559, issued to Lanson et al, discloses two remotely controlled antennas that are caused to independently rotate about their respective axes by gear arrangements that are controlled elsewhere by an operator. Application of this apparatus to optimization of antenna direction for receipt of VHF and UHF television signals is discussed.
A communications duplexer that uses one antenna for receiving and a second antenna, spaced apart from the first antenna, for transmitting or receiving is disclosed by Etherington in U.S. Pat. No. 4,361,905. A radio transmitter and receiver is selectively coupled to one antenna for transmitting and to either of the two antennas for frequency diversity receiving. The antennas are not physically exchanged for receiving purposes.
Beier et al disclose a direction finding system using two GPS antennas in U.S. Pat. No. 4,719,469. First and second GPS signals are received by the first and second antennas, respectively, from a GPS satellite, and these signals are processed through first and second Costas loops, respectively. A phase difference is then determined from the output signals from the two Costas loops, using a phase meter, and the direction of the pointing angle of the two-antenna array to the satellite is determined from straightforward geometric arguments.
A direction finding method and apparatus using two antennas rotating at the same distance about a common axis is disclosed by Carr et al in U.S. Pat. No. 4,845,502. The time varying signals are multiplied to produce a low frequency component and a high frequency component. The low frequency component is used to determine azimuthal and elevation angles of the transmitter relative to the common axis, and the high frequency component is used to determine the incoming signal amplitude and frequency.
In U.S. Pat. No. 4,933,682, issued to Vaughn, a point-to-point microwave communication antenna is disclosed that can position a signal null in an arbitrary direction in which signal interference occurs. Two identical, parallel antenna horns are spaced apart by an adjustable distance d=n.lambda. that is chosen to position a "deep null" (at least 40 dB down) at an angle corresponding to receipt of an undesired and strong interfering signal from another source. Application of the apparatus to electromagnetic signal interferometry is discussed.
A system for determining direction or spatial attitude using receipt of GPS signals is disclosed by Hwang in U.S. Pat. No. 5,021,792. Three or more GPS signal-receiving antennas are arranged collinearly with known distances of separation, and GPS signals are phase sampled. Positions of two of the antennas are then exchanged, and the phase sampling is then repeated. The antennas are then arranged in a collinear pattern with known distances of separation, and phase sampling is repeated. From these three sets of data, the spatial orientation or attitude of the plane containing the antennas is calculated, using equations set forth in the patent. The inventor asserts that, with this approach, it is possible to reduce the minimum number of GPS satellites required from four to three.
In U.S. Pat. No. 5,148,179, Allison discloses a method for resolving the phase integers that requires use of either the L1 or L2 PRN code phase (also known as pseudorange). Filtering is required in the process to reduce the errors due to PRN code phase multi-path. Both the L1 and the L2 carrier phase measurements are also required. The method can be used on moving platforms encountered in photogrammetry and hydrography.
Dynamic differential position determination, using carrier phase measurements at both the carrier frequencies f.sub.L1 and f.sub.L1, is disclosed by Hatch in U.S. Pat. No. 4,812,991. Hatch determines uncorrected pseudoranges from each of four or more satellites to a reference receiver of known position and to a roving receiver, both on the ground. Hatch also uses L1 and L2 carrier phase differences and filters the L1 and L2 pseudorange information, then further processes the filtered pseudorange data to obtain smoothed range data from each satellite to each receiver. Both L1 and L2 pseudoranges are required. Differences of the smoothed range data and theoretical range data are formed for each satellite-reference receiver combination to aid in determining the position of the roving receiver.
In the article, "The Antenna Exchange: One Aspect of High-Precision GPS Kinematic Survey", by Benjamin W. Remondi and Bernhard Hofmann-Wellenhof, presented at the International GPS Workshop in Darmstadt, Federal Republic of Germany, Apr. 10-13, 1988, a method is disclosed in which the phase integers are resolved by exchanging the positions of a reference receiver antenna and a roving receiver antenna, while maintaining satellite signal tracking. In the Remondi method, which is compared later with the disclosed invention, both the reference and roving receiver antennas are physically moved. Details of this method are given in the paper, "Kinematic and Pseudo-kinematic GPS", by Benjamin W. Remondi, presented at the International Technical Meeting of the Satellite Division of the Institute of Navigation, Colorado Springs, Colo., Sep. 19-23, 1988. This paper describes the same method, referred to as the Antenna Exchange method. Remondi suggests that use of five satellites is a practical minimum, and use of six or more is recommended. The process described with the aid of equations contained in this paper uses a triple-difference intermediate stage and requires computation of the relative position of the receiver antennas.
An accepted static survey field procedure orients the antennas at two ends of a baseline to the same arbitrary azimuthal angle relative to a fixed line drawn to one of the magnetic poles. This procedure is mentioned in "Trimble Model 4000SX GPS Surveyor, Installation and Repair Manual", part number 12395, page 12, published July 1987. To implement this procedure, a precision Geodetic Antenna, available from Ashtech, Sunnyvale, Calif., incorporates a compass with a single independent GPS antenna. See J. Ashjaee, "Precision Survey With Ashtech XII, The All-in-one, All-in-view", Proceedings of the Fifth International Geodetic Symposium on Satellite Positioning, Mar. 13-17, 1989, New Mexico State University, pp. 316-329. The antenna orientation is chosen to cancel the errors in relative position determination caused by misalignment between the physical centers and the electrical phase centers of the antennas and errors through movement of the phase centers as a function of satellite azimuth and elevation. The azimuthal angles need not be recorded and need not be utilized during any stage of the relative position determination, including determination of integer ambiguities. The azimuthal angle of one antenna relative to another antenna is not observed in this approach. Effects of antenna phase center movement have been investigated and reported by Michael Sims in "Phase Center Variation in the Geodetic T14100 GPS Receiver System's Conical Spiral Antenna", presented at the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, Md., Apr. 15-19, 1985.
Many of these methods require a time-consuming or complicated initialization procedure, or require triple-difference processing. What is needed is a method that permits accurate differential positioning by resolving the unknown phase integers associated with carrier phase measurements by relatively simple procedures. The method should be equally reliable in scenarios when the magnitude of the multi-path errors on PRN code phase measurements is large, and such large multi-path errors should not delay the initialization procedure. In addition, the method should work reliably with as few as four satellites with suitable geometry. In addition, the method should allow the easy addition of roving stations into an existing network of reference and roving stations without disturbing the differential positioning already in progress, by ensuring that the phase center of the reference station antenna remains fixed relative to the Earth.